{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T11:39:56Z","timestamp":1761824396853,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,15]],"date-time":"2022-06-15T00:00:00Z","timestamp":1655251200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Brazilian Federal Agency for Support and Evaluation of Graduate Education","award":["001","88887.310463\/2018-00","Proc. 2016\/24561-0","Proc. 2019\/23963-5","Proc. 309089\/2021-2"],"award-info":[{"award-number":["001","88887.310463\/2018-00","Proc. 2016\/24561-0","Proc. 2019\/23963-5","Proc. 309089\/2021-2"]}]},{"name":"CAPES-PrInt","award":["001","88887.310463\/2018-00","Proc. 2016\/24561-0","Proc. 2019\/23963-5","Proc. 309089\/2021-2"],"award-info":[{"award-number":["001","88887.310463\/2018-00","Proc. 2016\/24561-0","Proc. 2019\/23963-5","Proc. 309089\/2021-2"]}]},{"name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo (FAPESP)","award":["001","88887.310463\/2018-00","Proc. 2016\/24561-0","Proc. 2019\/23963-5","Proc. 309089\/2021-2"],"award-info":[{"award-number":["001","88887.310463\/2018-00","Proc. 2016\/24561-0","Proc. 2019\/23963-5","Proc. 309089\/2021-2"]}]},{"name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico (CNPq)","award":["001","88887.310463\/2018-00","Proc. 2016\/24561-0","Proc. 2019\/23963-5","Proc. 309089\/2021-2"],"award-info":[{"award-number":["001","88887.310463\/2018-00","Proc. 2016\/24561-0","Proc. 2019\/23963-5","Proc. 309089\/2021-2"]}]},{"name":"RUDN University Strategic Academic Leadership Program","award":["001","88887.310463\/2018-00","Proc. 2016\/24561-0","Proc. 2019\/23963-5","Proc. 309089\/2021-2"],"award-info":[{"award-number":["001","88887.310463\/2018-00","Proc. 2016\/24561-0","Proc. 2019\/23963-5","Proc. 309089\/2021-2"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Considering the growing interest in sending probes to the natural satellite Titan, our work aims to investigate and map natural orbits around this moon. For that, we use mathematical models with forces that have symmetry\/asymmetry phenomena, depending on the force, applied to orbits around Titan. We evaluated the effects due to the gravitational attraction of the Saturn, together with the perturbative effects coming from the non-sphericity of Titan (the gravitational coefficient J2) and the effects of the atmospheric drag present in the natural satellite. Lifetime maps were generated for different initial configurations of the orbit of the probe, which were analyzed in different scenarios of orbital perturbations. The results showed the existence of orbits surviving at least 20 years and conditions with shorter times, but sufficient to carry out possible missions, including the important polar orbits. Furthermore, the investigation of the oscillation rate of the altitude of the probe, called coefficient \u0394, proposed in this work, showed orbital conditions that result in more minor oscillations in the altitude of the spacecraft.<\/jats:p>","DOI":"10.3390\/sym14061243","type":"journal-article","created":{"date-parts":[[2022,6,19]],"date-time":"2022-06-19T21:19:26Z","timestamp":1655673566000},"page":"1243","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Lifetime and Dynamics of Natural Orbits around Titan"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4506-9971","authenticated-orcid":false,"given":"Lucas","family":"Ferreira","sequence":"first","affiliation":[{"name":"Grupo de Din\u00e2mica Orbital e Planetologia (GDOP), S\u00e3o Paulo State University (UNESP), Guaratinguet\u00e1 12516-410, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4939-013X","authenticated-orcid":false,"given":"Rafael","family":"Sfair","sequence":"additional","affiliation":[{"name":"Grupo de Din\u00e2mica Orbital e Planetologia (GDOP), S\u00e3o Paulo State University (UNESP), Guaratinguet\u00e1 12516-410, SP, Brazil"},{"name":"Institut f\u00fcr Astronomie und Astrophysik, Eberhard Karls Universit\u00e4t T\u00fcbingen, Auf der Morgenstelle 10, 72076 T\u00fcbingen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7966-3231","authenticated-orcid":false,"given":"Ant\u00f4nio","family":"Prado","sequence":"additional","affiliation":[{"name":"Academy of Engineering, Peoples\u2019 Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, 117198 Moscow, Russia"},{"name":"Postgraduate Division, National Institute for Space Research (INPE), S\u00e3o Jos\u00e9 dos Campos 12227-010, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1086\/144679","article-title":"Titan: A satellite with an atmosphere","volume":"100","author":"Kuiper","year":"1944","journal-title":"Astrophys. 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